The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

The alternative version of 12-TET only contains octaves of equal size in order to theoretically fulfil the definition of equal temperament (every semitone must be equal in terms of size).

I have designed the alternative version of 12-TET to account for the practice of stretching octaves which means it can be used as a framework for controlling inharmonicity. The size of each octave can be adjusted in accordance with the specific inharmonicity of a piano.------------------------------Roshan Kakiya------------------------------

Roshan: Do you imagine all piano octaves stretch the same (3.35 cents) or only the temperament?Original Message:Sent: 01-19-2019 16:16From: Roshan KakiyaSubject: 12-Tone Equal Temperament: An Alternative Approach

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

The alternative version of 12-TET only contains octaves of equal size in order to theoretically fulfil the definition of equal temperament (every semitone must be equal in terms of size).

I have designed the alternative version of 12-TET to account for the practice of stretching octaves which means it can be used as a framework for controlling inharmonicity. The size of each octave can be adjusted in accordance with the specific inharmonicity of a piano.------------------------------Roshan Kakiya

Roshan: Do you imagine all piano octaves stretch the same (3.35 cents) or only the temperament?Original Message:Sent: 01-19-2019 16:16From: Roshan KakiyaSubject: 12-Tone Equal Temperament: An Alternative Approach

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

5. RE: 12-Tone Equal Temperament: An Alternative Approach

This might be good in the digital realm but a piano is tuned with the specific partial makeup of each note, pianos are not tuned the same because each has differing partial strengths (inharmonicity). I can't see forcing this on a piano would have an acceptable outcome.

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.

The inharmonicity of a piano's strings needs to be dealt with in order to make a piano sound in tune. Piano tuners deal with the inharmonicity of a piano's strings by stretching Octaves.

In theory, the standard version of 12-Tone Equal Temperament corrects the Pythagorean Comma by narrowing all 12 Pure Fifths whilst preserving the purity of all 7 Octaves. In practice, the Octaves are stretched which means that the Octaves will not be pure in reality. This means that the theory of the standard version of 12-Tone Equal Temperament does not match the practice of stretching Octaves.

In theory, the alternative version of 12-Tone Equal Temperament corrects the Pythagorean Comma by widening all 7 Octaves whilst preserving the purity of all 12 Pure Fifths. This means that the theory of the alternative version of 12-Tone Equal Temperament does match the practice of stretching Octaves.